In many applications, the data of interest comprises
multiple sequences that evolve over time. Examples
include currency exchange rates, network traffic data,
and demographic data on multiple variables.
We develop a fast method to analyze such co-evolving
time sequences jointly to allow

(a) estimation/forecasting of missing/delayed/future values,

(b) quantitative data mining, discovering correlations

(with or without lag) among the given sequences, and

(c) outlier detection.

Our method, "MUSCLES", adapts to changing correlations among
time sequences. It can handle indefinitely long sequences
efficiently using an incremental algorithm and requires only
small amount of storage so that it works well with limited
main memory size and does not cause excessive I/O operations.
To scale for a large number of sequences, we present
a variation, the "Selective MUSCLES" method and
propose an efficient algorithm to reduce the problem size.

Experiments on real datasets show that MUSCLES outperforms
popular competitors in prediction accuracy up to 10 times,
and discovers interesting correlations.
Moreover, Selective MUSCLES scales up very well
for large numbers of sequences, reducing response time
up to 110 times over MUSCLES, and sometimes even improves
the prediction quality.